## Stability and instability of standing waves for 1-dimensional nonlinear Schrödinger equation with multiple-power nonlinearity.(English)Zbl 1180.35483

From the author’s abstract: We consider the stability and instability of standing waves for the following nonlinear Schrödinger equation: $iu_t+u_{xx}+f(u)=0,\quad t\geq 0,\;x\in \mathbb{R},$ where $$f(u)=\sum^m_{j=1}a_j| u|^{p_j-1}u$$ with $$a_j\in\mathbb{R}$$ and $$1<p_1<\cdots<p_m<\infty$$.

### MSC:

 35Q55 NLS equations (nonlinear Schrödinger equations) 35B35 Stability in context of PDEs
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